What are the value of the pixels of the convolved image?
The convolved image can be considered a feature map, where each new neuron represents some indication (or lack-there-of) of a feature in some receptive field of the original image, so no it does not need to be a valid image in the output.  

If you specifically care for it to be an image as an output, you can do a couple of things:  

1) normalize the produced feature map to some set range that youre working in (0-255 or 0-1)  

2) make the filter a valid probability distribution, and you know the output will stay in the same range as the input (ex: Gaussian filters)